Biophysics Jan 2013 Calorimetric Methods and Solution size determination. 22 Jan 2014

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1 Biophysics Jan Jan 2013 Calorimetric Methods and Solution size determination Part I - Calorimetry ITC Part II - How to determine macromolecular size 1

2 Thermodynamics Define the Gibbs free energy of a system : G = H - TS General expression for the change in free energy: ΔG = ΔH TΔS If ΔG < 0 the process is spontaneous. The relation between free energy and an equilibrium constant. ΔG 0 = RT lnk eq lnk eq = ΔG0 RT = $ ΔH 0 TΔS 0 & % RT ' ) = 1 $ ( R ΔS 0 ΔH 0 & % RT ' ) ( van t Hoff relation which tells us that the enthalpy of a reaction can be determined by measuring the equilibrium constant at a variety of temperatures: dlnk eq " d 1 % $ ' # T & = ΔH 0 RT 2

3 Isothermal Calorimetry Maintain one temperature, and measure heat (Enthalpy change) Change Concentration, Measure ΔH and K d -Drug Discovery -Protein-X interactions 3

4 ITC How does the experiment work? Only method that can directly measure the binding energetics of biological processes 4

5 Basic Thermodynamics of Protein Stability Range accessible by van t Hoff ΔCp - large and positive! Stability curve for a protein Curvature comes from: Tg and Tg are where ΔG=0 Th and Ts are where ΔH and ΔS = 0 d 2 ΔG = ΔCp dt 2 T Relationship at temperature of maximal stability. Note ΔH and ΔS are very steep functions of temperature that arises from ΔCp. The range over which many proteins are maximally stable can be limited. 5

6 Protein Stability: The difference of two very large numbers. Hydrophobic interactions weak ΔH folding +ve ΔH folding -ve Hydrophobic interactions most stable atoms closer together Kinetic energy separates atoms Robert M. Stroud

7 Typical Temperature Dependence for Macromolecular Binding Reaction ΔH ΔS K a K a on temperature Note the inverse dependence of ΔG ΔG changes less than 2 kcal/mol K a (25 C) = 10 9 ΔH = 5 kcal/mol ΔCp = -0.5 kcal/k mol K a (25 C) = 10 9 ΔH = -5 kcal/mol ΔCp = -0.5 kcal/k mol 7

8 Isothermal Titration Calorimetry (ITC) ΔH, contributions of individual interactions: van der Waals forces, (electrostatic, dipolar, hydrogen bonds in non-aqueous environs) etc. ΔS, Order changes: ΔSSOL, ΔSCONF, ΔSR,TR Hydrophobic Interactions, Hydrogen bonds in aqueous environment Electrostatics in aqueous 8

9 Isothermal Titration Calorimetry (ITC) Isothermal Titration Calorimetry (ITC) makes a direct measurement of the heat evolved or absorbed by the reaction that results from the mixing of two or more components. We consider the simple binding reaction of a ligand (L) being introduced to a protein (P) to form a simple binary complex (PL). The heat evolution or absorption by this reaction is dependent on the enthalpy and the number of moles of complex formed. q = ΔH 0 (T)n PL = ΔH 0 (T)V[PL] For this equilibrium with the association constant Ka: P + L Ka PL " Ka[L] % [PL] = [P T ] $ ' # 1+ Ka[L] & Where [L] is the unbound ligand concentration, [P T ] is the total concentration of protein, [P T ]= [P]+[PL], and [P] is the free protein. 9

10 Isothermal Titration Calorimetry (ITC) Combining the equations that describe q and [PL] we get: # Ka[L] & q = ΔH 0 (T)V[P T ]% ( $ 1+ Ka[L] ' The way this is written we cannot get both ΔH and Ka from the same measurement (if we only measure q). In an actual experiment a fixed quantity of ligand added to a fixed amount of protein at defined intervals. For each interval the area under the peak can be integrated to give the total heat of the interval, q i. $ Ka[L] q i = ΔH 0 (T)V[P T ] i Ka[L] ' i 1 & ) % 1+ Ka[L] i 1+ Ka[L] i 1 ( There still are too many things we do not know here. What we do know if the total amount of ligand added [L T ], or the ratio of, R = [L T ]/ [P T ] 10

11 We can fit this equation: Isothermal Titration Calorimetry (ITC) $ Ka[L] q i = ΔH 0 (T)V[P T ] i Ka[L] ' i 1 & ) % 1+ Ka[L] i 1+ Ka[L] i 1 ( If we substitute the following: [L] i = [L T ] [P T ] 1 Ka ± ([L T ] [P T ] 1 Ka) 2 4[L T ] 2 Once Ka and ΔH 0 are determined, ΔG 0 (T) can be calculated with: ΔG 0 (T) = RT lnka And the entropy from: ΔG 0 (T) = ΔH 0 (T) TΔS 0 (T) ΔG = ΔH - ΤΔSSOL - TΔSCONF - ΔSR,TR 11

12 The ITC experiment slope ~1/Kd Illustration of ITC reaction cell (A), data (B), and analysis by non-linear regression (C) ITC - heat-flux calorimeter - operates on the dynamic power compensation principle (i.e. how much power cal/sec to keep the temperature between sample 12 and reference cell constant)

13 ITC What do real data look like? An experiment with Calmodulin and a calmodulin binding peptide. How could one determine ΔCp? Why would looking at the temperature dependence be important? Wintrode and Privalov, JMB (1997) 13

14 ITC - Working range c = Ka[Mtot]n Working c range: Best range for determination 10 4 < Ka < 10 8 c = 1 Ka = 10 4 M -1, [M]T= 100 µm c = 10 Ka = 10 6 M -1, [M]T= 10 µm c = 1 c = 10 c = 10 c = 1 c = 1000 c = 1000 c = 1000 Ka = 10 8 M -1, [M]T= 10 µm Typical [M]T ~ 10 µm (Raising or lowering the solute concentration 14 can push the range. Nevertheless this factor is going to be the major limit)

15 ITC - Limits? Some Kas may be too weak to get a good binding curve without using unobtainable amounts of reagent. The other limit is if the interaction is too tight (~ 1 nm). Here, each addition results in complete binding of ligand ([PL] [L T ]. Since [P]=[P T ]-[P L ], when [L T ] [P T ], [P] 0 and the heat evolved will be zero. When [L T ] < [P T ], each titration will be exactly the same. This leads to a step function that cannot be fit accurately. 0.1 < K a [M] T <

16 ITC A way around the problem of tight binders. This reaction is too strong to measure accurately Exploit a thermodynamic cycle to determine the tight binding ligand. Sigurskjold 16 (2000)

17 Example I: Structure of the Ca V β-aid complex and analysis of protein-protein interactions Van Petegem et al. Nature (2004) 17

18 Ca V β-aid: Conserved mammals to jellyfish How to understand what is important? AID Identical Conserved Moderate Variable Ca V β 18

19 Alanine scan of AID-Ca V β interaction L438 L434 I441 I441 Y437 W440 ΔΔG (kcal mol -1 ) < W Y437 I Y437 Y437 W440 W440 Van Petegem et al. Structure 14: (2008) 19

20 An energetic hotspot dominates AID-Ca V β interactions kcal mol -1 > < 0.5 I343 L352 V341 R356 L392 M245 20

21 AID-ABP crucial hydrogen bond network Kd (nm) ΔH (kcal mol -1 ) ΔS (cal mol -1 K -1 ) N ΔΔG (kcal mol -1 ) CaV ± ± ± ± Y437F ± ± ± ± Y437A 5,263 ± ± ±

22 An energetic hotspot dominates AID-Ca V β interactions L352 I441 I343 M245 Y437 W440 L392

23 ITC - Limits? Low affinity Intermediate affinity High affinity A non-standard experiment: Here, the experiment is an attempt to measure accurately the association constant of a homodimeric protein. Working range is. 1 < K a [M 2 ] T < 1000 Kd = [M]2 [M 2 ] M 2 2M Heat associated with each titration $ q i = VΔH a &[ M] i M % [ ] i 1 F 0 M 0 v F 0 is fraction monomer in syringe 23 v is injection volume, V is cell volume V ' ) (

24 Specificity is coded in ΔH not ΔS ΔH driven Morrison equation Robert M. Stroud

25 DSC & ITC references Becktel, W.J. & Schellman, J.A. Protein Stability Curves Biopolymers 26: (1987) Weber, P.C. & Salemme, F.R. Applications of calorimetric methods to drug discovery and the study of protein interactions Curr. Op. Struct. Biol. 13: (2003) Velazquez-Campoy, A., Leavitt, S. A., & Freire, E. Characterization of Protein-Protein interactions by Isothermal Titration Calorimetry Methods Mol. Biol. 261:35-54 (2004) Velazquez-Campoy, A., & Freire, E. ITC in the post-genomic era? Priceless Methods Mol. Biol. 261:35-54 (2004) Falconer, R.J., Penkova, A., Jelesarov, I., & Collins, B.M. Survey of the year 2008: applications of isothermal titration calorimetry J. Mol. Rec. 23: (2010) (contains general review plus ~ 500 references to ITC experiments covering protein/ protein, peptide/protein, protein/drug. protein/lipid, protein/metal, protein/nucleic acid, nucleic acid/small molecule, etc. ) Sigurskjold, B.W. Exact analysis of competition ligand binding by displacement isothermal titration calorimetry Anal. Biochem. 277: (2000) 25

26 DSC & ITC references Becktel, W.J. & Schellman, J.A. Protein Stability Curves Biopolymers 26: (1987) Weber, P.C. & Salemme, F.R. Applications of calorimetric methods to drug discovery and the study of protein interactions Curr. Op. Struct. Biol. 13: (2003) Velazquez-Campoy, A., Leavitt, S. A., & Freire, E. Characterization of Protein-Protein interactions by Isothermal Titration Calorimetry Methods Mol. Biol. 261:35-54 (2004) Velazquez-Campoy, A., & Freire, E. ITC in the post-genomic era? Priceless Methods Mol. Biol. 261:35-54 (2004) Falconer, R.J., Penkova, A., Jelesarov, I., & Collins, B.M. Survey of the year 2008: applications of isothermal titration calorimetry J. Mol. Rec. 23: (2010) (contains general review plus ~ 500 references to ITC experiments covering protein/ protein, peptide/protein, protein/drug. protein/lipid, protein/metal, protein/nucleic acid, nucleic acid/small molecule, etc. ) Sigurskjold, B.W. Exact analysis of competition ligand binding by displacement isothermal titration calorimetry Anal. Biochem. 277: (2000) 26

27 Part II How we measure macromolecular size? Modern Detectors for total Mass of species SAXS (Small Angle X-ray Scattering) (Mass Spectrometry for later in the course) 27

28 Macromolecular Structures Growth in number and complexity of structures versus time Robert M. Stroud

29 I. Molecular sieving methods The size of a protein molecule determines the rate of its passage through a molecular sieve. Molecular sieves consist of small particles of materials that have a network of pores into which molecules of less than some given maximum size can penetrate. (cf. continuous media such as a polyacrylamide gel). 29

30 An estimate of size.. Migration through the gel reflects the Stokes radius of the protein. In order to figure out the molecular weight of a test protein, one needs a set of molecular weight standards. Test proteins may run anomalously if they are a very different shape from the standards (i.e. not spheres), or if they interact with the column. 30

31 SEC Tetra Detector Array (UV, LS, RI, IV) For the Purification and Characterization of Membrane Quantitative size Proteins aromatics 280nm amides 220nm = Concentration for known sequence, or known extinction coefficient =molecular mass dielectric =all species Viscosity reflects =mol shape = accurate molecular weights Estimation of intrinsically disordered protein shape and time-averaged apparent hydration in native conditions by a combination of hydrodynamic methods Karst et al., Methods in Mol Biol (2012)

32 Tetra Detector Array/Analysis C UV = UV/(K UV *da/dc) C RI = RI* RI sol /(K RI *dn/dc) M avg = K LS *K opt *LS 90º /(RI sol2 *C*(dn/dc) 2 ) Beer-Lambert Law Snell s Law Raleigh Equation for small molecules (< 1/20 of λ 670nm ) Detector Calibration Response Factors Ks Measured using stable protein with well known M, dn/dc and da/dc Shape and Size Detector (Differential Viscometer; measures Differential Pressure) IV= DP/C = dl/g (~~inversely α density) Newtonian Viscosity (liquid layers) applied to tubes using Poiseuille s Law V h = (M*IV)/2.5N A Einstein Vh for hard spheres = SEC Universal Calibration Principal V h = 4/3*R h3 π (volume of hydration) R h = [(3/10π)*IV*M/N A ] ⅓ 32

33 Crystal structure at 3.2Å resolution of the Sec61αγ from Pyrococcus furiosus heterotrimer coexpressed and assembled in vivo and copurified crystallization and optimization of diffraction quality from 25Å to 3.2Å SEC Sec61αβγ excess Sec61β&γ in micelles Seleno-MAD/MR Robert M. Stroud 2014 Membrane Protein Expression Center Pascal Egea & Robert Stroud PNAS 2010

34 Application (AQP4) Determine if Protein Detergent Complex can be concentrated before SEC Dictated by comparison of PDC and Micelle Retention Time (Detergent/lipid RT measured for all common buffer-sec systems) DP YES Dimer Monomer PDC No Excess OG micelle RALS RI 280nm PDC Excess OG micelle DP RALS 280nm RI RI inverted Superdex,40mM OG TDAgram post 40x 50kDa stir concentrate Superdex, 40mM OG TDAgram post 30kDa spin concentration PDC Homogenous tetramer Tetramer Globular (IV=0.05) with 5.7 nm Rh Binds 260 OG Contains 38mM excess OG in micelles Monomer 0.17 dn/dc Robert M. Stroud

35 Application 2. Can be applied to intrinsically unfolded proteins. Robert M. Stroud

36 Solu5on sca:ering and shape of molecules Do not need crystals, but much lower Resolu5on Solu5on averages all orienta5ons Can see different popula5ons in solu5on Can determine overall shape of species Can monitor 5me dependent conforma5on change micro sec to days Robert M. Stroud

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41 Robert M. Stroud SAXS determines accurate assembly state in solu5on, as shown for acetyl- CoA synthetase subunit Hura et al Nat Methods August; 6(8):

42 SAXS defines accurate shape and assembly in solu5on for unknown structures and can uncover unsuspected structural similarity. Experimental sca:ering curves for proteins with no known structural homolog (lez, color) were compared with calculated sca:ering Robert M. Stroud

43 Conceptual schema5c of solu5on sca:ering with focused XFELs. Sca:ering pa:erns may lose circular symmetry when a small number of par5cles are illuminated with femtosecond pulses from XFELs. The angular fluctua5ons increase the amount of informa5on in the sca:ering data and can be u5lized for ab ini5o structure analysis of biomolecules in solu5on. Advances in X- ray sca:ering: from solu5on SAXS to achievements with coherent beams Javier Pe rez1 and Yoshinori Nishino2 Current Opinion in Structural Biology 2012, Robert M. Stroud

44 Discussion paper Robert M. Stroud

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46 minimal ΔCp = inc Hphobic effect Robert M. Stroud

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49 less variability in Flap+ in a) the flap mutants regidify the flaps! Robert M. Stroud

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51 Companion paper.. Robert M. Stroud

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